Modelling stability of growth between mathematics and science achievement via multilevel designs with latent variable

In this thesis, a series of multilevel models was introduced to handle hierarchically structured data. A multivariate multilevel model was adopted for multivariate response data; a multilevel model with latent variables was utilized for the data with measurement errors; a multilevel growth model was applied to repeated measures data. Based on these models, we derived a multivariate multilevel growth model with latent variables to model the consistency among students and among schools in the rates of growth for "true" mathematics achievement and "true" science achievement after adjusting for measurement errors during the entire middle and high school years, with data from the Longitudinal Study of American Youth (LSAY). There was no evident consistency of growth among students, and the inconsistency was not much influenced by student characteristics and school characteristics. However, there was evident consistency among schools, and this consistency was influenced by student characteristics and school characteristics. The relationship between the rates of growth for "true" mathematics achievement and "true" science achievement was much more evident at the school level than at the student level.